Learn Hardcore Swahili: Baada ya zoezi, misuli yake huhisi uchovu kidogo. - After the exercise, her muscles feel a bit tired.

zoezi = an exercise, a (single) exercise / activity / test (singular)
mazoezi = exercises, or exercise (as an activity in general) (plural / collective)

Both are grammatically fine:

Baada ya zoezi, …
→ After the (specific) exercise, …
Baada ya mazoezi, …
→ After (doing) exercise / after the exercises / after working out, …

For “after exercise” in a general, workout sense, Baada ya mazoezi is extremely common.
Baada ya zoezi sounds more like one specific exercise or one session/test.

What exactly is misuli? Is it singular or plural, and what is the singular form?

Misuli is plural and means muscles.

The singular is msuli = a muscle.

msuli (singular) – one muscle
misuli (plural) – muscles

In this sentence, misuli yake = his/her muscles.
Swahili usually uses the plural here, just like English does.

Why is it misuli yake and not something like misuli wake or misuli zake? How would I say my / your / their muscles?

The possessive word has to agree with the noun class of misuli.

msuli / misuli belongs to the m-/mi- class (class 3/4).
For this class, the possessive prefix is ya-.

Then we add the person ending:

-ngu = my
-ko = your (sg.)
-ke = his/her
-tu = our
-o = their

So:

misuli yangu = my muscles
misuli yako = your muscles
misuli yake = his/her muscles
misuli yetu = our muscles
misuli yao = their muscles

wake would be used with class 1/2 (people), e.g. mtoto wake (his/her child), watu wake (his/her people).
zake is used with class 10 nouns (like ndizi zake – his/her bananas).

Even though misuli ends in -i, it’s not class 10 here; it’s the m-/mi- class, so the correct form is yake.

What does huhisi mean exactly, and why not use inahisi or anahisi?

The verb is hisi = to feel.

inahisi is normal present tense with a non-human subject (class 4 here):
- Misuli yake inahisi uchovu kidogo.
  → Right now his muscles feel a little tired.
huhisi uses the special hu- tense, which marks habitual / general actions:
- Misuli yake huhisi uchovu kidogo.
  → His muscles usually / generally / tend to feel a little tired.

So hu- gives the idea of a typical, repeated reaction, not just one specific moment.
That fits the meaning “After exercise, his muscles feel a little tired (as a usual thing).”

If misuli is non-human, shouldn’t the verb have ina- at the start? How does subject agreement work with hu-?

In normal present tense you would indeed use i- for misuli (class 4):

Misuli yake inahisi uchovu kidogo.
(i- is the subject prefix for class 4.)

But with the habitual tense hu-, Swahili doesn’t use an explicit subject prefix. The pattern is:

[Subject noun phrase] + hu- + verb

So:

Misuli yake huhisi uchovu kidogo.
(no i- in front of hu-)

The noun phrase misuli yake is still the subject; it’s just not marked again on the verb when using hu-.
So huhisi here already includes the idea of “(they) generally feel …”

Why does the sentence use uchovu (tiredness) instead of an adjective like “tired”? Can I say it with a verb like kuchoka instead?

Uchovu is a noun meaning tiredness / fatigue.
Swahili often uses hisi + noun of a feeling:

anahisi uchungu = he feels pain
wanahisi furaha = they feel happiness
misuli yake huhisi uchovu = his muscles feel tiredness

In natural English we turn that into an adjective: feel tired.

You can rephrase the sentence with the verb choka (to get tired):

Baada ya zoezi, misuli yake huchoka kidogo.
→ After exercise, his muscles get a bit tired.

Both ways are acceptable; your original sentence is just using the noun “tiredness” instead of a state verb.

Why is kidogo placed after uchovu? Could it go somewhere else?

When kidogo means “a little / a small amount” and modifies a noun, it normally comes after the noun:

maji kidogo = a little water
pesa kidogo = a little money
uchovu kidogo = a little tiredness

So uchovu kidogo literally means “a small amount of tiredness”, which we translate as “a little tired”.

kidogo can also modify a verb, and then it comes after the verb phrase:

alichoka kidogo = he got a bit tired
anaumia kidogo = it hurts a little

But *misuli yake huhisi kidogo uchovu is not natural.
In this sentence, kidogo is clearly quantifying the noun uchovu, so its usual place is after uchovu: uchovu kidogo.

Can I move baada ya zoezi to the end of the sentence?

Yes. Time expressions like baada ya zoezi are fairly flexible in position. Both of these are grammatical:

Baada ya zoezi, misuli yake huhisi uchovu kidogo.
Misuli yake huhisi uchovu kidogo baada ya zoezi.

Putting baada ya zoezi at the beginning slightly emphasizes the time (“After exercise, …”), but the meaning is the same.

How would I say “After exercising, his muscles feel a little tired” instead of “after the exercise”?

Use baada ya kufanya (ma)zoezi (“after doing exercise / after exercising”):

Baada ya kufanya mazoezi, misuli yake huhisi uchovu kidogo.
→ After exercising, his muscles usually feel a little tired.

You can also say:

Baada ya kufanya zoezi, misuli yake huhisi uchovu kidogo.

kufanya zoezi/mazoezi = to do exercise / to exercise / to work out.

Does yake mean his, her, or its here? How could I show the gender clearly?

yake by itself can mean his, her, or its. Swahili doesn’t mark grammatical gender the way English does.

So misuli yake could be:

his muscles
her muscles
its muscles (e.g. an animal, in the right context)

If you need to be explicit, you add a noun or pronoun:

misuli ya kijana huyo = that boy’s muscles
misuli ya msichana huyo = that girl’s muscles
misuli yake yeye mwanamke = her muscles (she, the woman)

But in normal sentences, context usually makes it clear whether yake is “his” or “her.”